Calculating-machine.



No. 825,363. PATENTED JULY 10, 1906.

J. VERMBHREN. CALCULATING MACHINE.

APPLICATION FILED SEPT. 2 1901.

2 BHEETS-SIQEET 1.

mflzess 6S java J07" No. 825,363. PATENTED JULY 10, 1906.

J. VERMEHRBN. CALCULATING MACHINE.

APPLICATION FILED SEPT. 20, 1901.

2 SHEETS-SHEET 2.

mhzess as. $2 VB/ILZ'OI" UNITED STATES PATENT OFFICE JQHANNES VERMEHREN,()F HELLERUP, DENMARK, ASSIGNORTO' AKTIESELSKABET VERMEHRENSREGNEMASKINEE, OF COPEN- HAGEN, DENMARK.

CALCULATING-MACHINE Specification of Letters Patent.

Patented July 10,1906.

Original application filed September 1, 1900, Serial No. 28,786, Dividedand this application filed September 20, I901.

I Serial No. '75,695.'

To all whom it may 001mm.-

- Be it known that I, JoHANNEs VERMEHREN,

friction or calculating members, one member cone-shaped, while the ofeach pair bein other one is shape as a disk or a ring whose edge runs onthe outer or inner surface of the conein frictional contact with it, sothat the disk or ring is rotated when the cone is rotated. The disk orring may be mounted in such a manner that its contact-points with thecone have a constant but adjustable distance from the apex of the coneor so that it during its rotation also has a lengthwise motion in thedirection of its axis, whereby its consecutive contact points with thecone form a curve the projection of which on the base of the'cone formsa logarithmic spiral. By the combination of said pairs of calculatingmembers with a number of counting apparatus the machine is able toperform multi- .plications and divisions of whole numbers and fractionsand multiplications, divisions, involutions, evolutions, andcalculations by means of logarithms. q

The accompanfying drawings ive diagrammatical views 0 the improvecIcalculatingmachine. I

Figure 1 shows a plane view of the machine desi ned for. multiplicationsand divisions of who e numbers and fractions; Fig. 2, a slightlydiflerent form of the machine designed formultiplications, divisi ns,evolutions, involutions, and calcula s by means of logarithms; and Fi 3,a front view of the machine in Fig. 1. ig. 4 is a plan of one sideof amodified form of'machine.

. In Fig. 1 a machine is shown having two pairs of calculating members aZ and a l, of which the disk-shaped members a and a are connected with acounting apparatus, res ectively, t and t, for registering the comp etcand partial rotation of the said members. The

it runs with its edge on the surface of the cone-shaped member Z (Z)and. that its contact-point with said cone may be set at any desireddistance r (r) from the apexof the cone Z (Z) by movin lengthwise thespindle c (0"), to which the disk a (o) is secured, and which spindle isoperatively connected with the corresponding countingapparatus t, (27.)The distance may be indicated by the disks themselves on scales 1) p,parallel with the spindles c c. When rotated, the cones ,Z Z rotate thedisks a a by friction, and they are mounted on spindles d d, which maybe rotated by means of cranks or handles 9 g. The spindles d d may berotated independently of each other or they may be coupled together, forinstance, by means of a clutch operated by a handle f, so that both thespin-v d disk a (a') ismounted in such a manner that set at zero Withoutturning the spindles c and c, and when now the crank g is turned (thespindles d and (1 being coupled together) the values of the indicationsof the two counting apparatus will be in the ratio of 1- to r. Themultiplication of a figure with a fraction is therefore easily performedby means of this simple machine. If, for example, it is required to take18% per cent. of a series of numbers (values)that is to say, to multiplythe same by fi z the two disks 0 a are set so that 1" equals sixteenand?" equals three, in which case the disk a, and consequently 'thecounting apparatus t, connected with a,

will rotate at or Q per cent. 18% per cent.

the speed of the diskn and the counting ap-' paratus t, connected witha. The counting apparatus t" shows in this case the 18% per cent. of thenumbers indicated by the count ing apparatus t. i

This mechanism presents great advanta es; s ecially for calculatingftheexchange va ue 0 bonds and the like. for example, one German mark iseighty-eight oere, Danish, and one French franc equals 72.5 oere, thedisks a and a. must be adjusted so as to make 1 equal eighty-eight and requal 72.5, so that the counting apparatus 13 will indicate the numbarof francs and the other one, i, the corresponding'number of marks butthe said arrangement may also be employed for general multiplications,as may be seen from the example quoted. If, for example, any givennumber is to be multiplied by sixty-seven, it

is the same as multiplying with the fraction It is obvious that themachine may be used for performing divisions also.

Instead of having the disks 0. a secured to the spindles c c thearrangement may also be such that the disks take their spindles alongwith them when they rotate, but can be moved lengthwise on the spindles,and of course the spindles c 0 must always be able to turn the countingapparatus t t when the disks are rotated by means of the cones. Theimproved machine may also be rovided with a greater number of pairs ofca culati'ng members than a Z and a l If, for example, four such pairsare used, it is feasible simultaneously to indicate dollars and centswith one counting apparatus and the corresponding values in marks,florins, and francs with the other three. The machine will thereforeprove to be of the reatest advantage for money changers and ankers.

In the form shown in Fig. 2 the disks a a, are secured to screw-threadeds indlesc c, which turn in screw-threaded earings, so that they movelengthwise when the disks are rotated. The cones Z Z are mounted asalready explained. As now the spindles c and 0 move lengthwise whenrotated, it will be seen that the consecutive points of contact of thepairs of calculating members will describe curves on the surface ofl Z,the vertical projections of these curves forming log arithmic spirals onthe bases of the cones.

it be assumed that cone Zis rotated at angle d-and that it upon radius1* takes the disku alon by friction at angle dc at the same time t atthe disk 1, has radius R, then we have by a similar consideration as inAmslers planimet'er:

m ma

of the height of the screw, so that H K d 1' d (p I d 1' I andsubsequently 18rd Q constant.

It follows that with said infinitely small movement the projection onthe base of the cone at the first and last point of contact be- 'tweenthe disk a and the cone Z always lies upon a line situated on the baseof the cone under a constant angle with the radius vector.

The logarithmic spiral has meanwhile just a constant angle between atangent and radius vector.

When the equation for a logarithmic spiral in polar coordinates iswritten and when for the sake of simplicity it is desired that the driftof the spiral on which all the projected points of contact are lyingshall begin at radius 1 and after ten full rotations end at radius 10 todetermine k and a, it is found that 1=7c 6 and 10=7c e whereof 7c=1 and10=e or r 1 a log e a= 10 21rZ0g. e where screw has nine fillets on thedistance which the screw 0 must shift lengthwise, whereas log. 7"

the point ofcontact between the disk a and the conelshifts from radius 1to radius 10, the radius R of the disk a may easily be figured out,since we have there H equals 1, for We have, as quoted above,

and by diiferentiation from theequation of the spiral:

log. r= 1O .27r We get 1 l g. e (11 1 7 d E) 10 27: that is.

1" d =1O 27:109. do", and therefore we again get l If be accepted ashaving this dimension and the cone Z or, as shown in Fig. 2, its axis(1, is combined with adisk which is caused to rotate at only one-tenthof the speed of that of Z, the part of a revolution of that diskrepresents the mantissa of logarithm of the figure which is shown by t.For example, if it shows 789 an angle 6) corresponds to this figure,which may be found from the equation wherefore 5; represents the part ofa whole revolution performed by the disk above referred to. If now thisdisk is combined with athirdcounting apparatus t the said part of therevolution may be read with still greater I accuracy.

It follows from the foregoing description that the counter t may beemployed to indicate the mantissa of the log. 1), supposing the countertindicates the figure p, and in .the same way a fourth counter tcombined with the cone Z in the same manner as the above-named countingapparatus t with the cone Z, may indicate themantissa of the log. q if Zshows the figure g. It is therefore rendered possible by adjusting thecounter t at the figure p so that the counter t indicates the mantissaof 10gb and by coupling afterward the counters t and t together, while ipoints at zero, and by then turning handle g so far that counter tindicates g to obtain thatthe counter t indicates the mantissa of lop+log g. By this means the counter-t wil e brought to indicate theproduct of p multi lied by g. This machine is therefore capab e of beingused for multi lications, and consequently it may be use for divisionsalso. If, however, the cones Z and Z are not coupled asshown in Fig. 2,but connected together in such a manner-for example, by means of cog edwheelsthat Z is caused to rotate at dou le the speed of Z, it is obviousthat the operator by means of counter t is enabled to indicate thesquare 5 dealing with extracting root may be perof sedond power ofany'figure shown by the counter t, and if the cones Z and Z are -con,nected together in such a manner that Z q is brought to rotate at threetimes the speed of Z the operator may find at the counter 25 the cube orthird'power of the figure shown at the counter t. The machine may aconsequently' be employed for calculations of the second and third owersof numbers also. Moreover, all calculations dealing with'raising anumber toa hi her power (therefore also the calculation 0 annuities) andthose formed by first adjusting the counter t on a number, say p,whereby the counter 15 will indicate the mantissa of log. p. If then thecounter t is adjusted to indicate the log. p, it is rendered possible toperform a multiplication or a division, respectively, with the numberindicating the higher power of which it is required to raise the saidfigure or with that representing the root to be extracted. As the resultof the operation a logarithm is found to which the counter t must beadjusted in order to indicate with the'counter t the number sought.

Generally speaking, one half of the machine may be used as a logarithmictable, the counter t indicating the mantissas of Briggss' logarithmswhich correspond to the numbers indicated by the counter t.

In order to insure that the projection onthe base of the cone of thepoints of contact between the members a and Z when connected by linesshall result in a logarithmic spiral and in order to avoid dependence onfriction between the two members, the circumference of disk a may beprovided with pointed teeth and the cone Zmay have correspondingcavitiesor holes the projection of which on the base of the cone when connectedby a curve form a logarithmic spiral. In Fig. 2 teeth are shown on thecircumference of the disks a a and holes in the cones Z Z. regularmotion of the disk 0. in its relation to the cone Z is thus insured bymeans of teeth and corresponding holes, it is also possible, if desired,to dispense with the screwthreads' of the spindle c of disk a and'withthe corresponding threads in the bearing, and it is even feasible, ifdesired, to cause the spindle c to partake in the rotary movement of.disk a, but without moving in its longitudinal direction. It is,however, also possible to construct the improved calculating-machine insuch a manner that the contact-points between the disk a and the cone Zhave a constant distance from the apex of the cone, while projection ofthe contact-points between the disk (1/ and the coneZ form a logarithmicspiral, or vice versa. In such case the counter i may be employed fordetermining the mantissas of the logarithms of the numbers indicated bythe other counter t, or .vice versa. The improved machine may also beprovided with a greater number of pairs of calculating members than a Zand a Z. By combining many such pairs of calculating members it ispossible to obtain results with more figures than hitherto. As sucharrangement, however, is well known, a further description is notnecessary. Instead of being mounted to work like a screw in its bearingthe s indle 0 might be fixed and be screwthreade so that the disk (1 maybe screwed along it like a nut; but in this case therotary motion of thedisk (1, must be transmitted to the counter t, for example ,by means ofa cyl- 9 5 If the inder C, mounted parallel to spindle c and ac tuatedby the pointed teeth of disk (1 engaging the cavities formed along asiral drawn upon the surface of the said cylin. er C. (See Flg. 4.) 1

It will be seen that the construction of this improvedcalculating-machine is based on a novel principle, which makes itsuperior to all other machines of this kind by reason of the fact thatso many different calculations may be performed on it and by reason ofthe high speed with which'it works.

Having now particularly described and ascertained the nature of my saidinvention and in What manner the same is to be performed, I declare thatwhat I claim is 1. In a calculating-machine, a main shaft, a number ofcone-shaped friction members carried thereby, a corresponding number ofdisks having their edges in contact one with each cone, rotary spindlesparallel with the slo ing surface of the corresponding cone and eachsupporting one of the said disks, and a calculating apparatusoperatively con nected with each spindle, substantially as described.

2. In a calculatin -machine, a main shaft, a number of cone-s ap edfriction members carried thereby, a corresponding number of disks havingt r edges 1n contact one with 7 each cone lengthwise-adjustable rotaryspinseaaee dles parallel with the slopingsurface of the correspondingcone andeach supporting one of the said disks, and a calculatingapparatus operatively connected with each spindle, substantially asdescribed.

3. In a calculating-machine, a main shaft, a number of primarycone-shaped friction members carried thereby, a corresponding number ofdisks having their edges in contact one with each cone, rotary spindlesparallel with the slopingsurface of the corresponding cones and eachadjustably supporting one of the said disks, and a calculating apparatusoperatively connected with each spindle, substantially as described.

4. In a calculating-machine, a main shaft,

a number of primary cone-shaped friction members carried thereby, acorresponding number of'disks having their edges in contact with eachcone, rotary screw-threaded spindles parallel with the sloping surfaceof the corresponding cone and each supporting one of the said disks, anda calculating apparatus operatively connected with each spindle,substantially as described.

In witness whereof I have hereunto set my hand in presence of twowitnesses.

JOHANNES VERMEHREN. Witnesses:

MARCUS MoLLER, MAGNUS JENSEN. 4

